A drive device of this type is known from DE 35 45 869 C2 or DE 198 23 730 A1. The roof module has two movable roof parts which are shiftable relative to the roof module between opening and closed positions with the aid of drive transmission cables. The drive transmission cables are driven by in each case one output pinion for each roof part, with the two output pinions being assigned to a common drive motor. In order to activate the two output pinions by means of the common drive motor, a distributing gearing is provided in DE 35 45 869 C2. In DE 198 23 730 A1, the transmission of drive from the common drive motor to one of the two output pinions is changed over via an electromagnetic change-over device.